In a semiconductor integrated device, for example a metal-oxide semiconductor (MOS) transistor, a substrate current may be used and may represent a hot electron effect. A hot electron effect may be a phenomenon that, when electrons travel from a source region to a drain region through a channel region in a MOS transistor, an electric field applied to the electrons in a channel around an end of the drain region may be maximized, and kinetic energy of the electrons may be significantly increased. Some electrons may go beyond an energy barrier at an Si—SiO2 interface and may intrude into an SiO2 film. The electrons with significant energy may be called hot electrons. Electrons with high energy, which may be hot electrons, may cause impact ionization in a high-electric-field region of a drain junction while traveling. Because of impact ionization, secondary electron-hole pairs may be generated. Of these, the electrons may move toward a drain region and may increase a drain current. In addition, holes may move toward a substrate according to an electric field, and may form a substrate current. Therefore, the extent to which a hot electron effect may occur may be analyzed based on a substrate current. That is, an increase in substrate current may indicate that a hot electron effect in a MOS transistor may be relatively more pronounced. An increase in a substrate current may affect electrical characteristics of a MOS transistor. For example, in a CMOS circuit, various problems, such as noise or latch-up, may occur. For this reason, an error may occur if a circuit is operated.
FIG. 1 illustrates a change in a substrate current depending on a gate voltage in a state where a drain voltage Vd in a related art MOS transistor may be maintained at 3.3 V, 2.75 V, and 2.2 V. Referring to FIG. 1, if a drain voltage in a related art transistor is maintained at a predetermined value or more, for example, when a drain voltage Vd may be at 3.3 V, substrate current may initially increase depending on a gate voltage. In addition, substrate current may decrease after a certain peak point. A reason may be as follows.
Initially, if a gate voltage is applied, a drain current may increase, and a number of electrons for an impact ionization may increase. If a gate voltage becomes excessively high, a MOS transistor may operate from a saturation region to a linear region. Therefore, a vertical electric field at a pinch-off point in a channel may decrease. As a result, an impact ionization ratio may decrease. A substrate current may be an important factor that may affect reliability of a product and output resistance. Therefore, in developing a semiconductor device, it may be necessary to accurately understand and predict characteristics of a substrate current. In addition, as semiconductor devices become more highly integrated, a hot electron effect may become more pronounced. Therefore, in developing a highly integrated semiconductor device, it may be important to predict what characteristics a substrate current may have in a MOS transistor.
Characteristics of a substrate current in a device, including a MOS transistor, may be predicted by modeling based on impact ionization. Many programs may be commercially available and may predict a substrate current of a device, including a MOS transistor. For example, SPICE may be an example of a design program that may use Berkeley Short-channel IgFET Mode (BSIM3) to predict a substrate current. A BSIM3-based substrate current prediction model may not accurately predict a substrate current for a high voltage device, such as a high voltage MOS transistor. A high voltage MOS transistor may have sufficient capability to endure a high voltage that may be applied to its drain, and may be commonly used in various power devices.
A high voltage MOS transistor may have a lateral double diffused MOS (LDMOS) in which a drain region may be lightly impurity doped, which may maintain a stability of a drain from the high voltage, and which may extend laterally. Characteristics of a substrate current in a device including a high voltage MOS transistor may be different from those in a device including a related art transistor.
FIG. 2 illustrates characteristics of a substrate current depending on a gate voltage in a high voltage MOS transistor where a drain voltage Vd may be maintained at 13.5 V, 11 V, 8.5 V, and 6 V. Referring to FIG. 2, in a high voltage device, if a drain voltage Vd is initially at 1.5 V, if a gate voltage increases, a substrate current may also increase (first region, 200). A substrate current may start to decrease after a certain peak point (second region, 210). In first region and second region, a high voltage device may have substantially the same characteristics as a device including a related art MOS transistor. If a gate voltage further increases, a substrate current may increase again (third region, 220). Such a third region may not be observed in a device such as a related art MOS transistor. As a result, it may be impossible to accurately predict a behavior of a substrate current in a high voltage device by modeling according to the related art.